PDA

View Full Version : Horizon Question

Andrew D
2010-Apr-01, 04:18 AM
Given a static Schwarzschild spacetime of ADM mass M, it is well known that no ingoing causal geodesic starting in the outer domain r > 2M will cross the event horizon r = 2M in finite Schwarzschild time

How does a black hole gain mass if no object can cross the horizon in a finite amount of time?

neilzero
2010-Apr-01, 05:28 AM
Infinite time does occur for the distant observer, but not for the time frame of the mass entering the event horizon. Since gravity travels at the speed of light, perhaps the increased mass will never be detected by the distant observer. Neil

TrAI
2010-Apr-01, 05:45 AM
How does a black hole gain mass if no object can cross the horizon in a finite amount of time?

Well, my guess would be that it gets in by falling in, doesn't notice the time dilation/space compression that much, since those are properties of a non inertial frame.

But I am not sure it is right to say it crosses the event horizon, it can cross the Schwarzschild radius, but from it's frame of reference it doesn't cross the event horizon, that would seem to be falling away below at the same rate. At least for a Schwarzschild black hole...

WayneFrancis
2010-Apr-01, 06:13 AM
I've asked this question to Prof Muller before. The issue of it getting to the EH isn't an issue. To an external observer the gravity from the mass can be treated as a point source. Even if the mass doesn't pass the EH from our point of view it still adds to the BH's total mass when looked at from an external observer. Also just like a black hole's EH doesn't grow from the centre out during formation the EH just IS at the radius determined by the spin and mass of the BH. Add enough mass to just above the EH of a black hole and the EH, to an external observer, can be thought of as bubbling out beyond where the in falling energy is. If you don't like that model just do the calculations and you'll see that with enough mass above the EH of a BH the total mass of the BH causes the EH to be at a greater distance.

dgavin
2010-Apr-01, 02:10 PM
Strickly speaking from and outside observers point of view. Whats would be likely seen is the mass/partiles aproaching ever closer to the BH, never quite reaching the event horision due to time dialation. What happens is there comes a point where the mass simply vanishes at the same moment the EH increases from the addition of more mass.

My guess is it's one of thouse cases where causality is violated in the outside observers frame, as the events are simultaeous. You couldn;t tell if the mass was abosorbed first, casuing the increas in EH size, or the EH increased in size to absorb the time frozen mass. From both inside the BH and from the masses point of view, the events happen in sequence, mass is absorbed then EH size increses by a tiny fraction of a fraction.

Andrew D
2010-Apr-01, 03:26 PM
What happens is there comes a point where the mass simply vanishes at the same moment the EH increases from the addition of more mass.

But this can never be measured by the observer, because the falling object only reaches the EH after an infinite amount of his time. Thus, an outisde observer would measure the mass of the obeject-black hole system, as long as the observer is located at a radius greater than that of the object. But the object would still never enter the black hole. The argument that the mass of the black hole increases in finite time for an external observer is like saying the mass of the Earth increases by the mass of the moon once one is at a greatter distance from the earth than the moon.

My guess is it's one of thouse cases where causality is violated in the outside observers frame, as the events are simultaeous. You couldn;t tell if the mass was abosorbed first, casuing the increas in EH size, or the EH increased in size to absorb the time frozen mass. From both inside the BH and from the masses point of view, the events happen in sequence, mass is absorbed then EH size increses by a tiny fraction of a fraction.

I don't follow. can you rephrase?

Andrew D
2010-Apr-01, 03:33 PM
Even if the mass doesn't pass the EH from our point of view it still adds to the BH's total mass when looked at from an external observer.

Of course, the mass of any matter within a system with any radius whos center is located at the singularity will gravitate as though all that mass is located at the singularity, but that doesn't mean the 'total mass' of the black hole is equal to the mass of the system. It just means that the mass of the system equals the mass of the black hole plus the mass of the rest of the matter in the system, and any observer outside the system measures that mass to be located at the singularity.

grant hutchison
2010-Apr-01, 03:46 PM
We can imagine infalling material building up in some sort of shell around the event horizon, according to the Schwarzschild observer. Although it takes forever for material to reach the Schwarzschild radius, in Schwarzschild coordinates, it gets very close very quickly: so this shell is very thin, and very close to the Schwarzschild radius.
Once the shell accumulates enough mass, it becomes impossible for photons to escape from the combined gravity of shell + black hole, and the absolute horizon simply jumps outwards, accommodating the new mass inside a larger event horizon, determined by the mass added to the black hole.
The absolute horizon is a global property of spacetime, separating photons that will escape to infinity from photons that will end at the singularity. So as soon as the existence of the infalling matter shell means that photons just outside the event horizon can't escape to infinity (because of the gravity of the shell), the absolute horizon "reaches out" to absorb the shell.
So the infalling matter doesn't need to cross the horizon: it just needs to get close enough to produce a great enough density to create a new horizon around itself, as WayneFrancis has described.

Grant Hutchison

tommac
2010-Apr-01, 04:18 PM
There was an interesting thread a few months back about the formation of a BH via collapse, I believe I started it. While I was hesitant about what was being stated, in the end there was enough there to show that time dilation cant stop the collapse of the star. At the point that the star becomes a black hole ... much of the mass is already inside the formed EH. For the rest the EH grows as the external rings of mass collapse in relatively quickly moving ( compared to the EH ) time ... as those rings collapse the EH expands past the mass that was "stuck in time" at the horizon. So while the matter outside the horizon will get stuck ... the EH itself does not seem to have that same limitation.

tommac
2010-Apr-01, 04:20 PM
Here are 8 pages of classic tommac

thanks Grant!

dgavin
2010-Apr-01, 07:01 PM
But this can never be measured by the observer, because the falling object only reaches the EH after an infinite amount of his time. Thus, an outisde observer would measure the mass of the obeject-black hole system, as long as the observer is located at a radius greater than that of the object. But the object would still never enter the black hole. The argument that the mass of the black hole increases in finite time for an external observer is like saying the mass of the Earth increases by the mass of the moon once one is at a greatter distance from the earth than the moon.

I don't follow. can you rephrase?

Well basically what I was saying the same thing as tommac, but in a different way.

As mass nears the point of "time frozen" at 1 phlank distance from the event horizon, what an outside observer would see would be something odd. He sees the mass "vanish" at the same time the EH exands to encompass the mass. This is the point where SR/GR breaks down in math, in that the cause (mass falling into the BH) and the effect (Event Horizon increasing in size) happen simultaneously to outside observers, which would be a causality violation in thier frame of reference.

And you are correct you would not be able to detect this moment from an outside observer, because of the causual violation.

Andrew D
2010-Apr-01, 08:33 PM
There was an interesting thread a few months back about the formation of a BH via collapse, I believe I started it. While I was hesitant about what was being stated, in the end there was enough there to show that time dilation cant stop the collapse of the star. At the point that the star becomes a black hole ... much of the mass is already inside the formed EH. For the rest the EH grows as the external rings of mass collapse in relatively quickly moving ( compared to the EH ) time ... as those rings collapse the EH expands past the mass that was "stuck in time" at the horizon. So while the matter outside the horizon will get stuck ... the EH itself does not seem to have that same limitation.

awesome.

We can imagine infalling material building up in some sort of shell around the event horizon, according to the Schwarzschild observer. Although it takes forever for material to reach the Schwarzschild radius, in Schwarzschild coordinates, it gets very close very quickly: so this shell is very thin, and very close to the Schwarzschild radius.
Once the shell accumulates enough mass, it becomes impossible for photons to escape from the combined gravity of shell + black hole, and the absolute horizon simply jumps outwards, accommodating the new mass inside a larger event horizon, determined by the mass added to the black hole.
The absolute horizon is a global property of spacetime, separating photons that will escape to infinity from photons that will end at the singularity. So as soon as the existence of the infalling matter shell means that photons just outside the event horizon can't escape to infinity (because of the gravity of the shell), the absolute horizon "reaches out" to absorb the shell.
So the infalling matter doesn't need to cross the horizon: it just needs to get close enough to produce a great enough density to create a new horizon around itself, as WayneFrancis has described.

So, once the matter trapped near the horizon reaches critical mass, the origional schw. radius becomes arbitrary while the schw. radius of the system (BH and the matter near the horizon) becomes the new radius? Does the outside obrserver measure this in a finite amount of proper time?

tommac
2010-Apr-01, 08:54 PM
Does the outside observe this occur in a finite amount of proper time? This is all relative to the external observer ... to the local observer things happen very quickly as they do not notice the time-dilation .... in other words if you were on the surface of the collapsing star you would not notice the time dilation and the star would just collapse. Not sure if I worded this correctly. But the time dilation is observed by the external observer.

astromark
2010-Apr-01, 09:08 PM
Not wanting to start a riot but... Its about 'your' point of view isn't it ?

From some distance away you see and detect the in falling object slow. Never reaching the BH. The object never did slow... it continued to accelerate all the way down. If the mass of the BH could be measured so accurately a increase would be detected while the object appeared to you still as not yet there. The use of the word relativity is handy for this circumstance. Its all a mater of separating what you might see from what is actually happening. They are not always the same thing...mark.

PS., Yes Tommac its just the way we say it...

Andrew D
2010-Apr-02, 02:22 AM
Not wanting to start a riot but... Its about 'your' point of view isn't it ?

From some distance away you see and detect the in falling object slow. Never reaching the BH. The object never did slow... it continued to accelerate all the way down. If the mass of the BH could be measured so accurately a increase would be detected while the object appeared to you still as not yet there. The use of the word relativity is handy for this circumstance. Its all a mater of separating what you might see from what is actually happening. They are not always the same thing...mark.

That makes sense.

WayneFrancis
2010-Apr-02, 02:48 PM
But this can never be measured by the observer, because the falling object only reaches the EH after an infinite amount of his time. Thus, an outisde observer would measure the mass of the obeject-black hole system, as long as the observer is located at a radius greater than that of the object. But the object would still never enter the black hole. The argument that the mass of the black hole increases in finite time for an external observer is like saying the mass of the Earth increases by the mass of the moon once one is at a greatter distance from the earth than the moon.

Yes but the centre is no longer the centre of the Earth.
In falling mass/energy doesn't have to pass through the EH to have its effect on warping space time added to the BH.

WayneFrancis
2010-Apr-02, 03:04 PM
Of course, the mass of any matter within a system with any radius whos center is located at the singularity will gravitate as though all that mass is located at the singularity, but that doesn't mean the 'total mass' of the black hole is equal to the mass of the system. It just means that the mass of the system equals the mass of the black hole plus the mass of the rest of the matter in the system, and any observer outside the system measures that mass to be located at the singularity.

Yes, and the EH is just a point where the Energy density is high enough to warp space in on itself.
There is one thing people fail to understand and I partly blame scientist. While it is true that to an external observer frame it might take an infinite amount of time to pass the EH by itself the actuality is for a stellar mass black hole you have to get VERY close to the EH before that type of time dilation start showing a very noticeable effect. I've done the calculations on these forums before and from memory for a 1 stellar mass black hole you have to get within like 1/4 inch of the EH to get a dilation like 1,000x. I'll see if I can find the thread in question.

So we'd see a faller initially get very close to the EH then slowly shift to red. So for a stellar mass black hole the matter will fall in close to the EH really quickly and even if it hovers outside the EH for a while eventually, given enough in falling mass/erergy, the EH will steadily grow and what an external observer saw as just above the EH would suddenly vanish.

WayneFrancis
2010-Apr-02, 03:06 PM
We can imagine infalling material building up in some sort of shell around the event horizon, according to the Schwarzschild observer. Although it takes forever for material to reach the Schwarzschild radius, in Schwarzschild coordinates, it gets very close very quickly: so this shell is very thin, and very close to the Schwarzschild radius.
Once the shell accumulates enough mass, it becomes impossible for photons to escape from the combined gravity of shell + black hole, and the absolute horizon simply jumps outwards, accommodating the new mass inside a larger event horizon, determined by the mass added to the black hole.
The absolute horizon is a global property of spacetime, separating photons that will escape to infinity from photons that will end at the singularity. So as soon as the existence of the infalling matter shell means that photons just outside the event horizon can't escape to infinity (because of the gravity of the shell), the absolute horizon "reaches out" to absorb the shell.
So the infalling matter doesn't need to cross the horizon: it just needs to get close enough to produce a great enough density to create a new horizon around itself, as WayneFrancis has described.

Grant Hutchison

I like your description more then mine!

WayneFrancis
2010-Apr-02, 03:12 PM
awesome.

So, once the matter trapped near the horizon reaches critical mass, the origional schw. radius becomes arbitrary while the schw. radius of the system (BH and the matter near the horizon) becomes the new radius? Does the outside obrserver measure this in a finite amount of proper time?

Yes.